Using the spin-2 completeness relation and differential equation alone, we have previously derived many elastic coupling relations [1]}, [2]}, [3]}, [4]}. For example, there are the elastic B-to-A formulas
\(b_{n^{\prime }n^{\prime }j} = \dfrac{1}{2}\big [2\mu _{n}^{2} - \mu _{j}^{2}\big ] a_{nnj} \hspace{35.0pt} b_{j^{\prime } n^{\prime }n} = \dfrac{1}{2} \mu _{j}^{2} a_{nnj} \hspace{35.0pt} b_{n^{\prime }n^{\prime }nn} = \dfrac{1}{3} \mu _{n}^{2} a_{nnnn} \) 
